This paper concerns the empirical basis of causation, and addresses the following issues: 1. the clues that might prompt people to perceive causal relationships in uncontrolled observations. 2. the task of inferring causal models from these clues, and 3. whether the models inferred tell us anything useful about the causal mechanisms that underly the observations. We propose a minimal-model semantics of causation, and show that, contrary to common folklore, genuine causal influences can be distinguished from spurious covariations following standard norms of inductive reasoning. We also establish a sound characterization of the conditions under which such a distinction is possible. We provide an effective algorithm for inferred causation and show that, for a large class of data the algorithm can uncover the direction of causal influences as defined above. Finally, we address the issue of non-temporal causation. 1 Introduction The study of causation is central to the understanding of hum...

Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UDGs) include models for spatial dependence and image analysis, while acyclic directed graphs (ADGs), which are especially convenient for statistical analysis, arise in such fields as genetics and psychometrics and as models for expert systems and Bayesian belief networks. Lauritzen, Wermuth, and Frydenberg (LWF) introduced a Markov property for chain graphs, which are mixed graphs that can be used to represent simultaneously both causal and associative dependencies and which include both UDGs and ADGs as special cases. In this paper an alternative Markov property (AMP) for chain graphs is introduced, which in some ways is a more direct extension of the ADG Markov property than is the LWF property for chain graph. 1 INTRODUCTION Graphical Markov models use graphs, either undirected, directed, or mixed, to represent...

this paper, Rumelhart presented compelling evidence that text comprehension must be a distributed process that combines both top-down and bottom-up inferences. Strangely, this dual mode of inference, so characteristic of Bayesian analysis, did not match the capabilities of either the "certainty factors" calculus or the inference networks of PROSPECTOR -- the two major contenders for uncertainty management in the 1970s. I thus began to explore the possibility of achieving distributed computation in a "pure" Bayesian framework, so as not to compromise its basic capacity to combine bi-directional inferences (i.e., predictive and abductive) . Not caring much about generality at that point, I picked the simplest structure I could think of (i.e., a tree) and tried to see if anything useful can be computed by assigning each variable a simple processor, forced to communicate only with its neighbors. This gave rise to the tree-propagation algorithm reported in [15] and, a year later, the Kim-Pearl algorithm [12], which supported not only bi-directional inferences but also intercausal interactions, such as "explaining-away." These two algorithms were described in Section 2 of Fusion.

One of the benefits of belief networks and influence diagrams is that so much knowledge is captured in the graphical structure. In particular, statements of conditional irrelevance (or independence) can be verified in time linear in the size of the graph. To resolve a particular inference query or decision problem, only some of the possible states and probability distributions must be specified, the“requisite information.” This paper presents a new, simple, and efficient “Bayes-ball ” algorithm which is wellsuited to both new students of belief networks and state of the art implementations. The Bayes-ball algorithm determines irrelevant sets and requisite information more efficiently than existing methods, and is linear in the size of the graph for belief networks and influence diagrams.

U.S.A. Normally, constraint networks are undirected, since constraints merely tell us which sets of values are compatible, and compatibility is a symmetrical relationship. In contrast, causal models use directed links, conveying cause-effect asymmetries. In this paper we give a relational semantics to this directionality, thus explaining why prediction is easy while diagnosis and planning are hard. We use this semantics to show that certain relations possess intrinsic directionalities, similar to those characterizing causal influences. We also use this semantics to decide when and how an unstructured set of symmetrical constraints can be configured so as to form a directed causal theory. 1.

A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combining prior knowledge, which might be limited solely to experience of the influences between some of the variables of interest, and data. In this paper, we first show how data can be used to revise initial estimates of the parameters of a model. We then progress to showing how the structure of the model can be revised as data is obtained. Techniques for learning with incomplete data are also covered.

Probabilistic networks can be constructed from a database of cases by selecting a network that has highest quality with respect to this database according to a given measure. A new measure is presented for this purpose based on a minimum description length (MDL) approach. This measure is compared with a commonly used measure based on a Bayesian approach both from a theoretical and an experimental point of view. We show that the two measures have the same properties for infinite large databases. For smaller databases, however, the MDL measure assigns equal quality to networks that represent the same set of independencies while the Bayesian measure does not. Preliminary test results suggest that an algorithm for learning probabilistic networks using the minimum description length approach performs comparably to a learning algorithm using the Bayesian approach. However, the former is slightly faster.

Abstract: Recently, we proposed a new method for representing and solving decision problems based on the framework of valuation-based systems. The new representation is called a valuation network, and the new solution method is called a fusion algorithm. In this paper, we compare valuation networks to decision trees and influence diagrams. We also compare the fusion algorithm to the backward recursion method of decision trees and to the arc-reversal method of influence diagrams.

INTRODUCTION This chapter surveys the development of graphical models known as Bayesian networks, summarizes their semantical basis and assesses their properties and applications to reasoning and planning. Bayesian networks are directed acyclic graphs (DAGs) in which the nodes represent variables of interest (e.g., the temperature of a device, the gender of a patient, a feature of an object, the occurrence of an event) and the links represent causal influences among the variables. The strength of an influence is represented by conditional probabilities that are attached to each cluster of parents-child nodes in the network. Figure 1 illustrates a simple yet typical Bayesian network. It describes the causal relationships among the season of the year (X 1 ), whether rain falls (X 2 ) during the season, whether the sprinkler is on (X 3 ) during that season, whether the pavement would get wet (X<F28.21

For nearly a century, investigators in the social sciences have used regression models to deduce cause-and-effect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work-- a principle honored more often in the breach than the observance.